class: top, inverse, title-slide .title[ # Neural Dynamic N-mixture Model ] .subtitle[ ## A deep learning framework for inferring demographic rates from count data ] .author[ ###
Speaker:
François Leroy (he/him)
Supervised by:
Marta Jarzyna
] .institute[ ###
The Ohio State University ] .date[ ### 2025-09-29 ] --- # Beyond abundance change <div class="center" style="margin:0;"> <h2 style="margin:0 0 0em; line-height:1.05; display:inline-block;"> Demographic rates </h2> </div> .pull-left[ * Changes in abundance are valuable, but demographic mechanisms offer deeper ecological insights * Species' extinctions event are the result of increasing difference between birth and loss * Demographic rates can be early warnings of species extinction * Monitoring survival and recruitment can help anticipate species' extinction and understand better the current biodiversity crisis ] .pull-right[ <br><br> <img src="data:image/png;base64,#images/slide1.png" width="2072" /> ] --- # Beyond abundance change <div class="center" style="margin:0;"> <h2 style="margin:0 0 0em; line-height:1.05; display:inline-block;"> Problem </h2> </div> .pull-left[ * Data for demographic rates models are individual based (i.e. *individual encounter history data*) * They are costly in resources and time * Individual identification is not equal for all taxa * Can be invasive/traumatic * Limited spatial and temporal extent ] .pull-right[ <div style="margin-right:-3.5em"> <img src="data:image/png;base64,#images/slide2.png" width="100%" /> ] --- # Beyond abundance change <div class="center" style="margin:0;"> <h2 style="margin:0 0 0em; line-height:1.05; display:inline-block;"> Using abundance to infer demographic rates </h2> </div> .pull-left[ * However, abundance data are available at large spatial and temporal scale * The idea of inferring birth/immigration (`\(\mu\)`) and death/emigration (`\(\lambda\)`) from experimental data is not new * While overall change in abundance gives information about `\(\lambda-\mu\)`, the volatility of the time-series provide information about `\(\lambda+\mu\)` making `\(\lambda\)` and `\(\mu\)` identifiable ] .pull-right[ <br> <img src="data:image/png;base64,#images/slide3.png" class="bigimg" /> ] .footnote[Wilkinson, 2011] --- # Dynamic N-mixture model <div class="center" style="margin:0;"> <h2 style="margin:0 0 0em; line-height:1.05; display:inline-block;"> Hierarchical Model </h2> </div> **Observation process** .pull-left[ `$$y_{i,j,t} \sim Binomial(N_{i,t}, p)$$` ] -- .pull-right[ `\(y =\)` observed abundance<br> `\(p =\)` detection probability ] **State process** .pull-left[ `$$N_{i,1} \sim Poisson(\lambda)$$` <br> `$$S_{i,t+1} \sim Binomial(N_{i,t}, \phi_{i,t})\\ R_{i,t+1} \sim Poisson(\gamma_{i,t})\\ N_{i,t+1} = S_{i,t+1} + R_{i,t+1}$$` ] .pull-right[ `\(\lambda =\)` abundance at `\(t = 1\)` <br> `\(\phi =\)` survival probability<br> `\(\gamma =\)` number of recruits ] .footnote[Dail & Madsen, 2011] --- # Neural hierarchical model .pull-left[ **Limitations of hierarchical framework** * Linear or simple polynomial effects of covariates, even though true ecological responses are often unknown *a priori* * MCMC algorithm scales poorly because inherently sequential, little possibility of parallelization * Sensitive to priors and initial values ] .pull-right[ **Limitations of Neural Networks** * Usually lack inferential power, making it less relevant for ecological insights * Doesn't distinguish between ecological process and imperfect detection ] -- .center[ <img src="data:image/png;base64,#images/joseph.png" width="70%" /> ] --- # Neural hierarchical model .center[ <img src="data:image/png;base64,#images/joseph.png" width="90%" /> ] <br> * Combines flexibility and scalability of neural networks with the inferential power of hierarchical models * Output activation function according to the parameter to infer (sigmoid for probability, exponential for counts) * Loss function: tailored from the model specific negative log-likelihood * Combines decades of development in hierarchical modelling for ecological data with the flexibility and predictive power of Neural Networks --- # Neural Dynamic N-mixture model .footnote[\* Krishnan et al. 2017] <div class="center" style="margin:0;"> <h2 style="margin:0 0 0em; line-height:1.05; display:inline-block;"> Deep Markov Model* </h2> </div> .pull-left-narrow[ <br> **State process** `$$\begin{align*} & N_{i,1} \sim Poisson(\lambda) \end{align*}$$` <br> `$$\begin{align*} & R_{i,t+1} \sim Poisson(\gamma_{i,t})\\ & S_{i,t+1} \sim Binomial(N_{i,t}, \phi_{i,t})\\ & N_{i,t+1} = S_{i,t+1} + R_{i,t+1} \end{align*}$$` **Observation process** `$$\begin{align*} & y_{i,j,t} \sim Binomial(N_{i,t}, p) \end{align*}$$` ] .pull-right-wide[ <div style="margin-right:-3.5em"> <br> <img src="data:image/png;base64,#images/NN_DNM.png" width="2807" /> ] --- # Example with the N-mixture model * Show the likelihood * You have to marginalize over n_max --- # The transition matrix * As it it a Hidden Markov Model, the likelihood involves a transition between time `\(t\)` and `\(t+1\)` * This is the bottleneck --- # Loss function of the DNMM --- # Optimization * Hidden Markov Model `\(\Rightarrow\)` Deep Markov Model (Krishnan et al., 2017) * Trade-off between memory use and speed * I choose fast implementation with heavy memory use --- # Simulated data --- # Results of the simulation --- # Fitting on real data --- # Next step * So far it is a simple MLP * Promising to use a CNN